User blog:Wythagoras/NEWS! I found a 22-state machine that beats G!
\(\Sigma(22) \gg f_{\omega+1}(2 \uparrow^{12} 3) > G\) 0 _ 1 r 21 0 1 1 l 21 1 1 1 l 1 1 _ 1 r 2 2 1 1 r 2 2 _ _ r 3 3 _ _ r 14 3 1 1 r 4 4 1 1 l 5 4 _ _ r 6 5 1 _ l 5 5 _ 1 l 1 6 _ _ r 14 6 1 1 r 7 7 _ _ r 6 7 1 1 l 8 8 1 _ l 9 8 _ _ l 15 9 _ _ l 10 9 1 1 r 11 10 1 1 l 9 10 _ 1 r 1 11 1 _ r 12 11 _ _ l 13 12 _ 1 r 11 12 1 1 l 13 13 1 1 l 13 13 _ 1 l 10 14 _ _ r 18 14 1 _ l 8 15 _ 1 l 16 15 1 _ l 1 16 1 1 l 17 16 _ 1 l 1 17 _ _ l 16 17 1 _ l 16 18 _ _ r halt 18 1 _ l 19 19 _ 1 l 20 19 1 _ l 15 20 1 1 l 19 20 _ 1 l 19 21 _ 1 l 0 21 1 _ l 14 State 1 is state 0 of Deedlit's expandal machine State x is state x of Deedlit's expandal machine for 2 ≤ x ≤ 17 Then, if the w+1 category is empty, it checks whether there is some in the w+2 category. Then it changes all empty categories (remember, the tape looks like 11111....11111_1_1_1_1...) to ones for the w+1 category. That is about \(f_{\omega}^{-1}(n)\) of the ones currently on the tape. State 0 and 21 are used to set the input. 1_11, where the head is on the first one and in state 14. Snapshots of the tape After 6 steps, state 14 1 11 ^ After 13 steps, state 2 111 11 ^ After 16 steps, state 18 111 11 ^ After 17 steps, state 19 111 1 ^ After 23 steps, state 1 1 1111 1 ^ After 59 steps, state 1 1 1 1 11 11 1 ^ After 1359 steps, state 10 11 1 1 1 1 1 1 1 111 111 111 111 111 11 1 1 1 ^ Bound \(\Sigma(22) > f_{\omega+1}(2 \uparrow^{12} 3) > G\) (See last tape) Poll Do you think I'm a TM specialist? yes no :Thanks. Wythagoras (talk) 18:58, August 6, 2014 (UTC) Poll 2 What is the smallest value of the Busy Beaver function that beats G, you think? 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 :Personally I think 11 or 12 (I voted for 12). I would be very suprised if someone could implent Ackermannian growth in 9 states, in other words, I'd be suprised if Sigma(9) > A(100). Wythagoras (talk) 18:58, August 6, 2014 (UTC) History September 9, 2010: r.e.s. proves that \(\Sigma(64) > G\) April 8, 2013: Deedlit11 proves that \(\Sigma(25) > G\) September 27, 2013: Wythagoras proves that \(\Sigma(24) > G\) using Deedlit11's results. October 6, 2013: Wythagoras proves that \(\Sigma(23) > G\) using Deedlit11's results. August 5, 2014: Wythagoras proves that \(\Sigma(22) > G\) using Deedlit11's results. Poll 3 When will \(\Sigma(21) > G\) be proven? August 2014 September 2014 later in 2014 first half of 2015 last half of 2015 2016 or 2017 later than 2017 never :This year hopefully :P. But not now. Wythagoras (talk) 18:58, August 6, 2014 (UTC) Poll 4 What is the smallest value of n such that \(\Sigma(n) > G\) will be proven within 5 years? 12 or less 13 14 15 16 17 18 19 20 21 22 :5 years is a long, long, long time. 5 years ago the wiki was barely created! Still, I think it is unreasonable to think we'd even come close to the real BB machines, so I think that Sigma(17) > G will be proven in five years, but if n is the number of states to beat G, I think that even Sigma(n+2) > G won't be proven within 15 years. Wythagoras (talk) 18:58, August 6, 2014 (UTC) Category:Blog posts